Question

1. calculate each of the following. leave answers as improper fractions in lowest terms.

a) ( 2\frac{1}{4} - \frac{1}{6} )
b) ( 2\frac{1}{2} \times 1\frac{3}{4} )
r3

Explanation:

Step1: Convert mixed number to improper fraction

$2\frac{1}{4} = \frac{2\times4 + 1}{4} = \frac{9}{4}$

Step2: Find common denominator for subtraction

Common denominator of 4 and 6 is 12.
$\frac{9}{4} = \frac{27}{12}$, $\frac{1}{6} = \frac{2}{12}$

Step3: Subtract the fractions

$\frac{27}{12} - \frac{2}{12} = \frac{25}{12}$

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Step1: Convert mixed numbers to improper fractions

$2\frac{1}{2} = \frac{2\times2 + 1}{2} = \frac{5}{2}$, $1\frac{3}{4} = \frac{1\times4 + 3}{4} = \frac{7}{4}$

Step2: Multiply the two fractions

$\frac{5}{2} \times \frac{7}{4} = \frac{5\times7}{2\times4} = \frac{35}{8}$

Answer:

a) $\frac{25}{12}$
b) $\frac{35}{8}$